1. If a pedestrian is in a marked crosswalk, cars may charge at but not actually hit pedestrians.
2. Drivers may disregard all pedestrians on pavement outside of marked crosswalks. Pedestrians step on unmarked pavement at their own risk.
3. If a pedestrian is on a sidewalk and moving towards a road, drivers may honk to warn the pedestrian not to proceed.

Crossings for pedestrians (referred to in this section as crossings) may be established on roads, or on subways constructed under roads, or on bridges constructed over roads, in accordance with this section." (Provision 121, Paragraph 1 of the Road Traffic Act)

However, there are supplementary rules which are not available online, and I had to get help at the Law Library to get a copy of "Road Traffic Act (Chapter 276, 121 and 140), Road Traffic (Pedestrian Crossings) Rules", which says that

"pedestrian crossing" means any crossing established for the use of pedestrians on a road, subway or bridge indicated by traffic signs, road markings, or otherwise as shown in any of the diagrams ..."

Except as provided in paragraph (5) [relating to physical incapacity], any pedestrian who is within 50 metres of either side of a pedestrian crossing ... shall make use of the pedestrian crossing for the purpose of crossing the road.

The driver of a vehicle who is in the process of turning his vehicle at a road intersection or junction where there is a pedestrian crossing shall stop his vehicle in order to give way to any pedestrian who is either crossing or is starting to cross the intersection or junction.

I didn't research the definition of right of way but this blogger claims pedestrians don't have it. This is apparently the norm in former British colonies.

So pedestrians have precedence in marked crosswalks, but nowhere else. I live on Bukit Timah Road, which is a major arterial, and simply to walk along the road on the sidewalk you must constantly cross driveways and side roads; none of these implied crossings are actually marked.

In contrast, here's the standard in the US:

The 2000 Uniform Vehicle Code and Model Traffic Ordinance (Uniform Vehicle Code) (Section 1-112) defines a crosswalk as:

1. "That part of a roadway at an intersection included within the connections of the lateral lines of the sidewalks on opposite sides of the highway measured from the curbs, or in the absence of curbs, from the edges of the traversable roadway; and in the absence of a sidewalk on one side of the roadway, the part of a roadway included within the extension of the lateral lines of the existing sidewalk at right angles to the centerline.
2. Any portion of a roadway at an intersection or elsewhere distinctly indicated for pedestrian crossing by lines or other markings on the surface."

(Federal Highway Administration)

And here's the relevant law for Washington State:

RCW 46.61.235.1 The operator of an approaching vehicle shall stop and remain stopped to allow a pedestrian or bicycle to cross the roadway within an unmarked or marked crosswalk when the pedestrian or bicycle

So, Singapore needs to either change its laws or paint a whole bunch of lines. And lest you think the latter is implausible, in the last few weeks the government has been sending crews to embed yellow textured mats in the curb cutouts. I assume this is to help blind people (of whom I've met or seen exactly one in public in all of Singapore. I think I've seen all of one or two wheelchairs, powered or otherwise; like most of Asia, the norm is for handicapped people to stay out of sight). Don't misunderstand: I applaud accessible infrastructure. I just wonder why they couldn't throw some zebra stripes down while they were at it.